A fundamental issue in the design of a wireless sensor network is to devise mechanisms to make efficient use of its energy. The information about the amount of available energy in each part of the network is called the energy map and can be useful to increase the lifetime of the network. In this work, we address the problem of constructing the energy map of a wireless sensor network using prediction-based techniques. The performance of the approaches to construct the energy map is evaluated through simulation. When simulation is used to evaluate the performance of the energy map construction or any other energy related problem, we have to know how the energy dissipation happens in nodes. To this end, we also present an energy dissipation model that is used to simulate the behavior of a sensor node in terms of energy consumption. Simulation results indicate that prediction-based techniques are more energy-efficient than a solution in which no prediction is used. We also investigate how the energy map can be used to construct an energy-efficient data dissemination algorithm.